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Express"],"published-print":{"date-parts":[[2026,7,13]]},"abstract":"<jats:p>Sensorless adaptive optics avoids a dedicated wavefront sensor, but closed-loop correction then depends on inferring aberrations from noisy focal-plane point-spread functions (PSFs) under finite latency and deformable-mirror (DM) constraints. This difficulty becomes acute in time-varying turbulence, where the commanded correction can be applied to a wavefront state that is already outdated. We present a closed-loop sensorless adaptive optics framework that combines single-frame PSF-to-modal estimation with delay-aware constrained control. A hybrid CNN-Transformer regresses 28 residual Zernike coefficients from noisy PSFs, and an autoregressive predictor with online parameter adaptation and fractional-step forecasting aligns the estimate with the effective actuation instant. The delay-aligned residual is then embedded in a constrained model predictive controller that enforces DM amplitude and slew-rate limits. Simulations over multiple turbulence strengths show that the learned estimator provides informative single-frame modal estimates, while the proposed NN+AR+MPC scheme improves loop stability, reduces residual phase RMS, and maintains higher Strehl ratio than both direct control and non-predictive MPC. The advantage grows with turbulence strength, indicating that temporal misalignment, rather than static estimation error alone, is the dominant limiter in the strong-turbulence regime. These results position delay-aware constrained optimization as a practical ingredient for robust high-speed sensorless adaptive optics.<\/jats:p>","DOI":"10.1364\/oe.601838","type":"journal-article","created":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T15:23:17Z","timestamp":1782228197000},"page":"25694","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Time-varying constraint optimization for sensorless adaptive optics systems driven by deep PSF-Zernike estimation"],"prefix":"10.1364","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-9396-9888","authenticated-orcid":true,"given":"Xingxin","family":"Fu","sequence":"first","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingtai","family":"Cao","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiyong","family":"Wu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingyu","family":"Xie","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,2]]},"reference":[{"key":"oe-34-14-25694-R1","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1038\/s43586-021-00066-7","type":"journal-article","volume":"1","author":"Hampson","year":"2021","journal-title":"Nat. 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